The use and understanding of mathematics is a crucial component of the physical sciences. Much work has been done in physics education research and science education more broadly to determine persistent difficulties with mathematics. This work has led to the development of numerous problem solving strategies aimed at helping learners approach…

Described is a graduate level engineering course on functional analysis offered at Purdue University. The course restricts itself to linear problems, specifically analysis of linear operators on vector spaces. Key applications in the course demonstrating the utility of abstract formulations are presented. (BT)

Discusses the emergence of chaos as a major scientific subject and its place in historical, scientific, and technological context. Three sections provide (1) an overview of the scientific paradigm; (2) a review of the ideology of classical mechanics; and (3) examples of classical systems behaving in peculiar, nonintuitive manners. (MDH)